Abstract: Much of the research on fluid dynamics is concerned with the phenomena of boundary layers and of turbulence. Both of these physical phenomena are associated with flows in the large Reynolds number regime and therefore are directly related with the mathematical study of the vanishing viscosity limit. Vanishing viscosity limits are an active ¨¢rea of research, focusing both on boundary-related issues, motivated by boundary layers, and on bulk flow issues more closely related to turbulence. The purpose of this minisymposium is to showcase current developments along both these lines, primarily focusing on describing the behavior of solutions of the Navier-Stokes and related system when viscosity is very small.

MS-We-D-13-113:30--14:00Vanishing viscosity limit and related problems of the incompressible flow under the helical symmetryNiu, Dongjuan (Capital Normal Univ.)Abstract: Helical symmetry is invariance under a one-dimensional group of
rigid motions generated by a simultaneous rotation around a fixed axis and trans-
lation along the same axis. In this talk we study the limits of three-dimensional helical viscous and inviscid incompressible flows in an infinite circular pipe as the viscosity and helical parameters vanish, repectively. In addition, the well-posedness of weak solutions to three-dimensional Euler equations are also mentioned.

MS-We-D-13-214:00--14:30Approximation of 2D Euler Equations by the Second-Grade Fluid Equations with Dirichlet Boundary ConditionsZang, Aibin (Yichun Univ.)Abstract: We prove three results. First, we establish convergence of the solutions of the second-grade model to those of the Euler equations provided $\nu = \mathcal{O}(\alpha^2)$, as $\alpha \to 0$, Second, we prove equivalence between convergenceand vanishing of the energy dissipation in a suitably thin region near the boundary, in the asymptotic regime $\nu = \mathcal{O}(\alpha^{6/5})$, $\nu/\alpha^2 \to \infty$ as $\alpha \to 0$.Finally, we obtain an extension of Kato's classical criterion to the second-grade fluid model.

CP-We-D-13-314:30--14:50CONTINUOUS DEPENDENCE ESTIMATE FOR STOCHASTIC BALANCE LAWS DRIVEN BY LEVY NOISEBiswas, Imran (Tata Inst. of Fundamental Research)Abstract: We are concerned with multidimensional stochastic balance laws driven by Levy
processes. Using BV solution framework, we derive explicit continuous dependence estimate on the nonlinearities of the entropy solutions. This result is used to show the error estimate for the stochastic vanishing viscosity method. In addition, we establish fractional BV estimate for vanishing viscosity approximations in case the the noise coefficient depends on both the solution and spatial variable.

CP-We-D-13-414:50--15:10The viscosity method for the homogenization of soft inclusions
Yoo, Minha (National Inst. for Mathematical Sci.)Abstract: In this talk, we consider periodic soft inclusions $T_\epsilon$ with periodicity $\epsilon$ where the solution $u_\epsilon$ satisfies semi-linear elliptic equations of non-divergence in $\Omega_\epsilon = \Omega \setminus T_\epsilon$ with a Neumann data on $T_\epsilon$.
The difficulty lies in the non-divergence structure of the operator where the standard energy method based on the divergence theorem can not be applied. The main object is developing a viscosity method to find the homogenized equation satisfied by the limit of $u_\epsilon$, called as $u_0$, as " approaches to zero. We introduce the concept of a compatibility condition between the equation and the Neumann condition on the boundary for the existence of uniformly bounded periodic first correctors. The concept of second corrector has been developed to show the limit $u_0$ is the viscosity solution of a homogenized equation.